As described in the Introduction, recent development within the area of Stein's method [1]} and [2]} have led to the ability to extend the diffusion method originally presented in [3]} to general manifolds. This particular construction of Stein's method, however, relies upon a sufficient condition which links the geometry of the manifold with the probability density \(p = e^{-\phi }\) , namely that
\(\mathrm {Ric}+ \mathrm {Hess}^\phi \ge 2\kappa g\) 
